Amplitude Modulation

Amplitude Modulation

Table of ontents Modulation theory... 3 Amplitude modulation... 4 Modulation Index... 6 Power in an AM waveform... 9 Double Side Band Suppressed Carrier... 10 Single Sideband Modulation (SSB-AM)... 10 Vestigial Sideband Amplitude Modulation (VSB AM)... 11 Appendix... 1 Pratial AM modulators... 1 The hopper modulator... 1 Non linear devies... 15 SSB generation... 16 Integrated iruit modulators... 17 AM Demodulation tehniques... 0 The diode detetor... 0 Synhronous AM detetion... Double Sideband Suppressed Carrier... 4 Joseph A. Zammit 008

Modulation theory A sine wave is represented as follows v ( t) = ACos( πft+ φ( t)) The symbols A, f and Φ(t) all represent parameters that an be modulated in the arrier waveform in order to arry information. The modulation shemes are known as: A Amplitude Modulation f Frequeny Modulation Φ(t) Phase Modulation Modulation is important sine it lets any portion of the radio frequeny spetrum used to transmit data. Here we are talking about analog modulation i.e. the transmission of analog signals, mostly audio and video signals. Also the method of transmission will vary aording to the portion of the radio frequeny spetrum used. The type of modulation used depends on the part of radio frequeny spetrum used and the bandwidth needed for the partiular appliation. Analogue modulation ontinuously varies the arrier with the modulating signal. Digital Modulation swithes the arrier on/off with the digital signal applied to the input. Joseph A. Zammit 008 3

Amplitude modulation Amplitude Modulation known as AM is one of the oldest and simplest forms of analogue modulation. Here the amplitude of the arrier waveform is hanged in sympathy with the information being transmitted. The amplitude of the arrier is made proportional to the instantaneous amplitude of the information signal. The following symbols are used throughout the text f, w Carrier frequeny and angular veloity respetively f m, w m Modulating frequeny and angular veloity respetively v Output voltage v m Modulating Voltage Let A be K + v m (t) where K is the un modulated arrier amplitude and v m (t) is the modulating signal. The modulating signal is expressed as v m (t) = acos(πf m t). Therefore the modulated signal beomes v ( t) = [ K+ acos( πf t)] Cos( πft) m v ( t) = K[1 + mcos( πf t)] Cos( πft) m m is the depth of modulated and represents how muh the AM waveform has been modulated. m is defined as modulating signal amplitude m= = unmodulated arrier amplitude a K For the AM waveform not to be distorted, m < 1 Expanding equation v (t) trigonometrially v ( t) = K[1 + mcos( πf t)] Cos( πft) m v ( t) = KCos [ ( πft) + mcos( πf tcos ) ( πft)] m Expanding 1 Using CosACosB= [ Cos( A+ B) + Cos( A B) ] m m v ( t) = K Cos(πft ) + Cos( π ( f fm ) t) + Cos( π ( f+ fm ) t) Joseph A. Zammit 008 4

An AM wave looks as follows Thus an amplitude modulated waveform ontains the following omponents f The arrier frequeny f + f m A frequeny omponent f m higher than the arrier f - f m A frequeny omponent f m lower than the arrier This is shown graphially below V Vm/ Vm/ f-fm f f + fm The amplitude of the sidebands is half the amplitude of the modulating waveform If v m (t) is replaed by a series of tones suh as speeh than the modulating waveform beomes Joseph A. Zammit 008 5

v ( t) = acos( πft) + acos( πft) + acos( πft) m Than the modulated arrier beomes 1 1 3 3 vm ( t) = acos n ( πft n ) n= 1 v ( t) = K 1 + m acos n ( πft n ) Cos( πft ) n= 1 The frequeny spetrum now beomes V Vm/ Vm/ f-fm f f + fm The total bandwidth is twie the bandwidth of the modulating signal This is also alled Double Side Band Amplitude Modulation (DSB-AM) Modulation Index The modulation fator is the ratio between the modulated and unmodulated arrier waveform. It an be expressed in various ways r.m.s value of V m ( t) m= r.m.s value of unmodulated arrier V ( t) Joseph A. Zammit 008 6

Vm ( V + Vm ) ( V Vm ) m= = V ( V + V ) + ( V V ) m= m m Maximum voltage - Minimum voltage Maximum voltage + Minimum voltage Example A arrier waveform v = 5Sin(8 x 10 6 )V is amplitude modulated by the signal v m = Sin(3 x 10 3 )V. Calulate the depth of modulation. The modulation index an be alulated as Vm m= = = 0.4= 40% V 5 For a general omplex waveform of a modulating signal v m (t) m = n= 1 v a n Example A arrier waveform v = 1Sin(5 x 10 6 ) is amplitude modulated by the signal v m = 5Sin(3 x 10 3 ) + 3Sin(1 x 10 3 )V. Calulate the depth of modulation. The r.m.s of the modulating signal is 5 + 3 = 4.13 4.13 m= = 0.485= 48.5% 1 If the waveform is modulated by a retangular waveform than the number of sinusoidal omponents in the waveform will be extremely large. Thus the r.m.s. value of the modulated waveform beomes Joseph A. Zammit 008 7

V T vdt 1 V m = 1 T = + 0 T m = m + m + m T 1 3 The sum of the individual modulation indexes in the omplex waveforms Example An 8V peak arrier wave is amplitude modulated by a square waveform of peak value 5V. Calulate a) the r.m.s. of the unmodulated waveform b) Depth of modulation a) The maximum value of the modulated waveform is 13V and the minimum value is 3V. Therefore for half the periodi time the amplitude is 13V and for the other half it is 3V. Hene T 1 T V = 13 Sin wtdt + 3 Sin wtdt T 0 T Using the Identity Sin 1 T 1 T 169 9 V = (1 Cos wt ) dt+ (1 Cos wt ) dt T 0 T The integration of Cosw over half a period is 0 V = 1 T T 0 θ = Cos θ T 84.5dt+ 4.5dt T ( T ) 1 V = 84.5 T+ 4.5 T T V = 44.5 V = 6.67V Joseph A. Zammit 008 8

b) To find the modulation index 8 m 6.67= 1+ T m = 0.884or 88.4% T Power in an AM waveform The total power in an AM waveform is the power in the arrier and the total power in the sidebands. The total power developed over a resistane R is P T V V m = = 1+ R R T W Carrier Power Side Band Power The transmission effiieny is the ratio of Sideband power (whih onveys useful information) and the total transmitted power. It is given by mt η= 100% + m The maximum effiieny of η is 33.3% when m T has a value of 1. Thus DSB-SC is very ineffiient. Example A 10kW arrier wave is amplitude modulated to at depth of 70%. Calulate the total sideband power and express it as a perentage of the total radiated power. From the power equation the total radiated power is T PT 3 0.7 = 10 10 1+ = 1.45kW Hene Sideband power is 1.45 10 =.45kW Expressed as a perentage of the total sideband power this is 19.68% Joseph A. Zammit 008 9

Double Side Band Suppressed Carrier As seen in the setion above a lot of the AM s waveform power is used in the arrier. Atually the arrier arries no information at all relevant to the signal being transmitted. Also in the presene of noise arrier power will add to the total noise reeived by the system. If the arrier is removed or suppressed in amplitude than the overall effiieny is inreased. The disadvantage of suh a system is the inreased omplexity in the detetor. This is known as DSB-SC (Double Side Band Suppressed Carrier). The modulated signal is represented as : m m v ( t) = Cos[ π ( f fm) t] + Cos[ π ( f+ fm) t] Representation of DSB-SC Single Sideband Modulation (SSB-AM) In DSB-SC the arrier was suppressed as it was arrying no useful information. It an be notied as well that the information transmitted in the lower sideband is the same as the signal in the upper sideband. Thus if one of the sidebands is to be suppressed there will be no loss of information. Single Sideband modulation Joseph A. Zammit 008 10

This is also known as SSB-AM. With SSB the bandwidth required for an AM system has been halved and therefore more information an be arried. The reeiver omplexity has now been inreased as it is harder to demodulate the signal. It is very popular with radio amateurs. Vestigial Sideband Amplitude Modulation (VSB AM) This is used for wideband modulating signals and signals that have a DC omponent that annot be eliminated. The bandwidth of a VSB-AM system an extend up to 5.5MHz in a television system. Applying a onventional DSB-AM system the bandwidth will extend to 11MHz whih is ineffiient. This is exessive in regard of transmission bandwidth and ost. Thus VSB-AM is a ompromise between DSB-AM and SSB-AM. The reeiver is muh simple than an SSB reeiver. V Vm/ f 1.5MHz f + fm f + 5.5MHz VSB-AM modulation Joseph A. Zammit 008 11

Appendix Pratial AM modulators It is diffiult to implement an AM modulator without giving the rise to unwanted sidebands whih must be filtered off before the AM signal being transmitted. For large power transmitters requiring good linearity, output stage modulation is employed. The modulator omprises of a lass B audio amplifier whih drives a lass C radio frequeny amplifier. The output is rih in harmonis and by using a tuned filter a fairly undistorted amplitude modulated signal may be obtained with an effiieny of about 80%. The RF arrier wave is obtained from a very stable rystal osillator and for high stability it is separated by a buffer amplifier. A suitable d.. power supply is also required to provide energy for the transmitter. A typial medium wave transmitter operates at a power level of about 50-100kW for broadast speeh and musi Audio I/P Class B Audio Class C RF amplifier RF Osillator The hopper modulator The hopper modulator or ring modulator is a ommon type of modulator. A diagram is shown below Joseph A. Zammit 008 1

Cos(w t) is a square wave. During the positive half yle f(t) is swithed on to the other side. When Cos(w t) is 0 the waveform is swithed off. The bandpass filter will remove higher frequeny omponents whih are not needed. The orresponding waveforms are shown below This is a theoretial model of a hopper modulator. A popular onfiguration is the double-balaned ring modulator. The modulator is popular as it does not require ideal omponents, provided that they have mathed harateristis (i.e. use the same part numbers). Joseph A. Zammit 008 13

Assuming that e i (t) is 0. During the positive half yles diodes D 1 and D will ondut and the point a is onneted to the out put transformer seondary. If the seondary of the referene transformer is aurately entre tapped and if the impedanes of D 1 and D are idential than no urrent will flow through the output transformer and no voltage will be developed at the output. During the next half yle D 3 and D 4 ondut and point b is onneted to the input through the opposite half yle of the output transformer seondary. Again no urrent will flow and no output will result. Thus we see that the arrier is suppressed. Now let e i (t) have the modulating input. Let us apply a positive polarity input signal whose peak amplitude is muh smaller than that of the referene e R. On the positive half-yles of Cosw t, point a is essentially at ground potential and a urrent will flow upward through half of the output transformer seondary, induing a positive output voltage. On the negative half-yles of Cosw t, point b is essentially at ground potential and a urrent will flow downward through the opposite half of the output transformer seondary, induing a negative output voltage. The peak positive and negative output voltages will be idential for a given fixed signal amplitude if the output transformer is aurately entre tapped. Therefore we have developed a signal that alternates in sign at a rate determined by the arrier frequeny and whose amplitude is proportional to the input signal amplitude. For DSB-SC modulation to our Joseph A. Zammit 008 14

1 [ e t ] max < ( ) [ e ( t)] i R MAX In pratie, an imbalane between diode harateristis and inauraies in the transformer entre taps will result in non-ideal performane and arrier leakage. Balaning ontrols an be added to fully tune out arrier leakage. Non linear devies Amplitude modulation an also arise in non linear systems. Diodes are good examples of non linear devies and may be used as a modulator. The following balaned modulator uses non linear devies to generate a DSB-AM. The non linearity an be approximated by the following power series it ( ) = aet ( ) + ae ( t) + ae ( t) +... 3 1 3 Referring to the above figure. By the transformer ations e ( t) = Coswt+ f ( t) 1 e ( t) = Coswt f ( t) Retaining up to the power of e (t) the urrent than beomes [ ] [ ] [ ] [ ] i ( t) = a Coswt+ f ( t) + a Coswt+ f ( t) 1 1 i ( t) = a Coswt f ( t) + a Coswt f ( t) 1 Joseph A. Zammit 008 15

For a resistive load e 0 (t) the net voltage is [i 1 (t) i (t)]r the output is a ( ) ( ) 4 ( ) f ( t) a 1 [ i t i t ] R= ar f t Coswt+ i Semiondutor diodes may be used as non linear devies suh as modulators. The performane of this type of modulator as for the ring modulator is dependant on how lose the harateristis of the diodes an be mathed. This is from a lass of balaned modulators. SSB generation The generation of SSB signals is more omplex as it requires to filter both the arrier and the lower side band. A system using balaned modulators is shown below Balaned Modulator F(t) F(t)Cos(wt) Cos(wt) + Σ ΦSSB(t) -90º -90º - F(t) Balaned Modulator F(t)Sin(wt) This system is very effiient and used for low frequeny generation and digital generation of SSB. Problems arise with the 90º phase shifters as they must provide a onstant phase for all the signal bandwidth. Therefore suh systems have very restrited bandwidths Joseph A. Zammit 008 16

Integrated iruit modulators Several semiondutor ompanies produe Integrated iruit modulators, based on the Gilbert ell a disrete transistor multiplier. Motorola produes an Integrated iruit modulator, the MC1496. This is a very versatile hip that provides modulation and de-modulation funtions. A full treatment of the IC is not possible here and the datasheet needs to be onsulted. The heart of the hip is the Gilbert Cell It onsists of differential amplifiers that multiply the signal. Motorola Appliation note AN531/D desribes in detail the operation of this Integrated iruit. It has 300MHz operating bandwidth suffiient for most appliations. The following shemati is of an AM modulator Joseph A. Zammit 008 17

It produes standard Double Sideband Bandwidth modulation. The amount of arrier in the output is adjusted by means of the arrier adjust potentiometer. Both the arrier input and the Modulating Signal Input have to be in the milli-volt levels for orret operation. The shemati below is a lassial DSB-SC modulator using the MC1496. Joseph A. Zammit 008 18

The iruit has differential outputs. Only one needs to be used for the final amplifiation stage. So far all iruits have been using dual supplies. The iruit below uses a single supply for modulation. Joseph A. Zammit 008 19

AM Demodulation tehniques Detetion or demodulation is the proess of reovering the intelligent signals from an amplitude-modulated wave. Most radio reeivers employ a diode detetor and most SSB systems use one type or other of balaned modulator. The diode detetor The diode detetor iruit onsists of a diode in series with a parallel resistorapaitor network. It is the simplest form of detetor found. It forms a lass of detetors alled non-oherent detetors. A non oherent detetor is not synhronized in phase with the transmitter If an un-modulated arrier wave is applied to the iruit the first positive half-yle of the wave will ause the diode to ondut. The diode urrent will harge the apaitor to a voltage slightly less than the peak value of the input signal. At the end of this half-yle the diode ease to ondut and the apaitor starts to disharge through the load resistor, R, at a rate determined by the time-onstant, CR seonds, of the disharge iruit. This time-onstant must be large ompared with the periodi time of the arrier wave to ensure that the apaitor does not disharge too muh during me following negative half-yle. The time-onstant for the harging of the apaitor is CR seonds, when r is the forward resistane of the diode. If the arrier wave is now amplitude modulated, the voltage aross the diode load will vary in sympathy with the envelope of the modulated arrier provided that the time onstant CR is small enough. The apaitor must be able to disharge rapidly enough for me voltage aross it to follow those parts of the modulation yle where the modulation envelope is dereasing in amplitude. See below for the effets of different CR onstants. Joseph A. Zammit 008 0

The apaitor voltage falls until a positive half-yle of the input signal makes the diode ondut and reharge the apaitor. When the modulation envelope is dereasing over one positive half-yle is of lower peak value than the preeding half-yle and the apaitor is reharged to a smaller voltage, If the time-onstant of the disharge path is too long, relative the periodi time of the modulation signal, the apaitor voltage will not be able to follow the troughs of the modulation envelope; that is, the deay urve passes over the top of one or more input voltage peaks, as sown by the dotted line In me above diagram. It an be shown that for this distortion to be negligible the maximum time-onstant is given by CR= 1 m πfm where m is the depth of modulation, f is the maximum modulating frequeny. The voltage developed aross the diode load resistor had three omponents a) a omponent at the wanted modulating signal frequeny b) a d. omponent that is proportional to the peak value of the un-modulated wave ) omponents of the arrier frequeny and harmonis of the arrier The basi detetor iruit must therefore be modified to prevent omponents b) and ) reahing the audio amplifier. The d.. omponent is removed with a series apaitor and the r.f omponents by a suitable RC filter. Two possible arrangements are shown below Joseph A. Zammit 008 1

D1 C1 R1 C R C3 R3 Diode detetion tehniques are good but for more demanding reeption synhronous tehniques must be employed. Synhronous AM detetion Ordinary envelope detetion for a.m. has several disadvantages. Many of these are overome by using a form of detetion known as synhronous detetion. This operates using what is essentially a beat frequeny osillator and mixer in very muh the same way as in the detetion of s.s.b. and morse. To ensure that the beat frequeny osillator is on exatly the orret frequeny it is synhronized to the inoming arrier frequeny. Synhronization of the arrier an be ahieved in a number of ways. A narrow band filter an be used to extrat the arrier and then this an be mixed with the inoming signal. This is the most obvious method, but it has the drawbak that the arrier has to be positioned on exatly the orret frequeny for it to operate orretly. Alternatively a phase loked loop an be used. The loop will lok onto the inoming arrier and generate a signal whih an be fed into the mixer. A third method feeds the inoming signal into a very high gain amplifier. If the gain is suffiiently high then iruit will limit, removing the modulation and leaving only Joseph A. Zammit 008

the arrier. This is then mixed with the original signal to regenerate the original audio. This last method is the heapest and it does not have the limitations of a very limited band of operation of the filter method. A low pass filter is used to reprodue the original audio signal Using a synhronous detetor muh lower levels of distortion an be ahieved. In addition to this the effets of seletive fading whih are often enountered on the short wave bands an be minimized. As a result this form of detetion is used in many high grade ommuniations reeivers. Mixer Low pass FIlter Audio Output Narrow band Filter Narrow band filter Method Mixer Low pass FIlter Audio Output Phase Loked loop Phase loked Loop Method Mixer Low pass FIlter Audio Output High gain limiting amplifier Hard Limiter Method Joseph A. Zammit 008 3

Double Sideband Suppressed Carrier Although Double Sideband Suppressed Carrier (DSB-SC.) is very seldom used, it is inluded here for the sake of ompleteness. Oasionally it is used by radio amateurs beause it is simpler and heaper to make a DSB-SC. transmitter than a full SSB. one, beause it does not need the expensive filtering required by SSB. To demodulate DSB-SC. the most onvenient method is simply to use the filter in the reeiver to remove one of the sidebands. Then it an be demodulated as if it were SSB. in the normal way. To demodulate DSB-SC, making full use of both of the sidebands requires more ompliated iruitry. Methods of demodulating DSB-SC require the arrier to be re-inserted, but unlike SSB, it has to be on exatly the right frequeny. To ahieve this it is possible to detet a small amount of arrier if any is transmitted and then amplify this. If no arrier is transmitted then it is still possible to generate it from the two sidebands. One way of doing this is to pass the signal through a square law devie suh as a diode. This produes a term whih is at twie the arrier frequeny. This an then be divided and used to demodulate the signal. Another method is named the Costas loop named after its inventor. This uses the system shown below and is onsiderably more ompliated in its operation. Joseph A. Zammit 008 4